Sludge, which includes solid material and considerable water, can be continually processed by placing it on a belt where it is vibrated to spread it and encourage gravitational drainage through the belt and capillary drainage from the inside of the sludge to the under surface of the belt, to thereby thicken the sludge. Further continuous processing can be accomplished by placing the thickened sludge on a cloth belt that passes in a convoluted path between rollers which squeeze the sludge lying on the belt. The pressing operation requires occasional removal of the belt to clean it and the rollers, so after reassembly the apparatus can operate efficiently. A processing apparatus that enabled a single processor to be readily changed between configurations useful for dewatering or pressing, and which also facilitated rapid disassembly of the rollers and belt in the pressing configuration for cleaning and rapid reassembly, would be of considerable value.